Higher June 2019 Paper 2 Q12
12 \(ABCD\) is a trapezium.
Diagram NOT accurately drawn
Calculate the perimeter of the trapezium.
Give your answer correct to 3 significant figures.
(4)
| Scheme | Marks |
|---|---|
\((ED =)\;\dfrac{16.7}{\tan 43}\) (=17.90855…) or \((CD =)\;\dfrac{16.7}{\sin 43}\) (= 24.48686…) | M1 |
\((ED =)\;\dfrac{16.7}{\tan 43}\) (=17.90855…) and \((CD =)\;\dfrac{16.7}{\sin 43}\) (= 24.48686…) | M1 |
| 16.7 + 21.2 × 2 + ‘24.5’ + ‘17.9’ (= 101.495…) | M1 |
| 101 | A1 |
| (4) | |
| (4 marks) |
Notes
M1: for a correct method to find length \(CD\) or \(ED\)
(\(E\) is the point on line \(AD\) from where a vertical line is drawn downwards from point \(C\))
NB. Sine rule may be used
M1: for a correct method to find both \(CD\) and \(ED\) or
use of Pythagoras theorem
\((CD =)\;\sqrt{16.7^2 + \text{``}{17.90\ldots}\text{''}^2}\) (= 24.48686…)
\((ED =)\;\sqrt{\text{``}{24.48\ldots}\text{''}^2 - 16.7^2}\) (=17.90855…)
NB. Sine rule must be in the correct form to give the answer
M1: (dep on M2) complete method with no extra sides
A1: accept 101 – 102